Score : 400 points
There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.
Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.
You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.
To help Tak, find the number of ways to go to Cell N, modulo 998244353.
Input is given from Standard Input in the following format:
N K L_1 R_1 L_2 R_2 : L_K R_K
Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.
5 2 1 1 3 4
4
The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.
There are 4 possible ways to get to Cell 5:
5 2 3 3 5 5
0
Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5. Print 0.
5 1 1 2
5
60 3 5 8 1 3 10 15
221823067
Note that you have to print the answer modulo 998244353.